[Paper Review] Comparing Cross Correlation-Based Similarities

Luciano da Fontoura Costa|arXiv (Cornell University)|Nov 8, 2021

Neural Networks and Applications22 references7 citations

TL;DR

This paper proposes and systematically compares multiset-based cross-correlation methods using real-valued Jaccard and coincidence indices against classic cross-correlation for template matching. The coincidence-based method outperforms others by producing sharper, narrower peaks and suppressing secondary matches, especially under noise, while a hybrid approach combining classic cross-correlation first enhances robustness to high noise levels.

ABSTRACT

The real-valued Jaccard and coincidence indices, in addition to their conceptual and computational simplicity, have been verified to be able to provide promising results in tasks such as template matching, tending to yield peaks that are sharper and narrower than those typically obtained by standard cross-correlation, while also attenuating substantially secondary matchings. In this work, the multiset-based correlations based on the real-valued multiset Jaccard and coincidence indices are compared from the perspective of template matching, with encouraging results which have implications for pattern recognition, deep learning, and scientific modeling in general. The multiset-based correlation methods, and especially the coincidence index, presented remarkable performance characterized by sharper and narrower peaks while secondary peaks were attenuated, which was maintained even in presence of intense levels of noise. In particular, the two methods derived from the coincidence index led to particularly interesting results. The cross correlation, however, presented the best robustness to symmetric additive noise, which suggested a new combination of the considered approaches. After a preliminary investigation of the relative performance of the multiset approaches, as well as the classic cross-correlation, a systematic comparison framework is proposed and applied for the study of the aforementioned methods. Several results are reported, including the confirmation, at least for the considered type of data, of the coincidence correlation as providing enhanced performance regarding detection of narrow, sharp peaks while secondary matches are duly attenuated. The combined method also resulted promising for dealing with signals in presence of intense additive noise.

Motivation & Objective

• To evaluate and compare multiset-based cross-correlation methods using real-valued Jaccard and coincidence indices against classic cross-correlation in template matching.
• To assess the robustness of these methods under varying levels of additive noise.
• To identify optimal configurations for pattern recognition and deep learning applications where similarity detection is critical.
• To propose a hybrid method combining classic cross-correlation with multiset-based indices to improve performance under high noise.
• To establish a systematic framework for quantitative comparison of cross-correlation performance across multiple metrics.

Proposed method

• Adapts the real-valued multiset Jaccard and coincidence indices to define new cross-correlation operations for signal similarity detection.
• Applies these similarity-based correlations to template matching tasks using synthetic and real signal data.
• Introduces a hybrid method where classic cross-correlation is applied first to denoise signals before applying multiset-based correlations.
• Employs a systematic performance comparison framework using multiple quantitative metrics, including peak sharpness, secondary peak attenuation, and noise robustness.
• Uses principal component analysis (PCA) to visualize and compare the sensitivity and dispersion of performance outcomes across methods.
• Defines performance indices such as peak width, signal-to-noise ratio of main peak, and suppression ratio of secondary peaks to objectively rank methods.

Experimental results

Research questions

• RQ1 How do multiset-based cross-correlation methods using Jaccard and coincidence indices compare to classic cross-correlation in terms of peak sharpness and secondary peak suppression?
• RQ2 What is the relative robustness of each method under high levels of additive noise?
• RQ3 Can combining classic cross-correlation with multiset-based methods improve performance in noisy environments?
• RQ4 Which of the multiset-based methods—Jaccard or coincidence—yields superior overall performance for template matching?
• RQ5 How do the performance characteristics of these methods vary across different signal types and noise levels?

Key findings

• The coincidence-based cross-correlation method produced the sharpest and narrowest main peaks, significantly outperforming both the real-valued Jaccard and classic cross-correlation methods.
• Secondary matching peaks were substantially attenuated in the coincidence method, indicating superior discrimination between true and false matches.
• Classic cross-correlation demonstrated the highest robustness to symmetric additive noise, particularly at high noise levels.
• The proposed hybrid method—applying classic cross-correlation before the multiset-based approach—showed enhanced performance in high-noise scenarios, especially for smooth templates.
• Principal component analysis revealed that the coincidence and Jaccard methods exhibited higher dispersion in performance space, indicating greater sensitivity to signal shape and noise variations.
• The results confirm that multiset-based correlations, particularly the coincidence index, offer a compelling alternative to classic cross-correlation in pattern recognition and deep learning contexts due to superior peak resolution and noise-aware suppression.